How do you find the derivative of #y= arctan[(x^2-1)^(1/2)] + "arccsc"(x)#?

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How do you find the derivative of #y= arctan[(x^2-1)^(1/2)] + "arccsc"(x)#?

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Answer 1 · 2015-09-15T16:35:47

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Explanation:

#y'=1/(((x^2-1)^(1/2))^2+1)1/2(x^2-1)^(-1/2)2x+(arcsin(1/x))'#
#=1/(x^2-1+1)1/2(2x)/sqrt(x^2-1)+1/sqrt(1-(1/x)^2)(-1/x^2)=#
#=x/(x^2sqrt(x^2-1))-1/(x^2sqrt((x^2-1)/x^2))=#
#=1/(xsqrt(x^2-1))-1/(xsqrt(x^2-1))=0#

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How do you find the derivative of #y= arctan[(x^2-1)^(1/2)] + "arccsc"(x)#?

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